orthax.laguerre.lagval

orthax.laguerre.lagval(x, c, tensor=True)Source

Evaluate a Laguerre series at points x.

If c is of length n + 1, this function returns the value:

\[p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x)\]

The parameter x is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either x or its elements must support multiplication and addition both with themselves and with the elements of c.

If c is a 1-D array, then p(x) will have the same shape as x. If c is multidimensional, then the shape of the result depends on the value of tensor. If tensor is true the shape will be c.shape[1:] + x.shape. If tensor is false the shape will be c.shape[1:]. Note that scalars have shape (,).

Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.

Parameters:

  • x (array_like, compatible object) – If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.

  • c (array_like) – Array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of c.

  • tensor (boolean, optional) – If True, the shape of the coefficient array is extended with ones on the right, one for each dimension of x. Scalars have dimension 0 for this action. The result is that every column of coefficients in c is evaluated for every element of x. If False, x is broadcast over the columns of c for the evaluation. This keyword is useful when c is multidimensional. The default value is True.

Returns:

values (ndarray, algebra_like) – The shape of the return value is described above.

See also

lagval2d, laggrid2d, lagval3d, laggrid3d

Notes

The evaluation uses Clenshaw recursion, aka synthetic division.

Examples

>>> from orthax.laguerre import lagval
>>> coef = [1,2,3]
>>> lagval(1, coef)
-0.5
>>> lagval([[1,2],[3,4]], coef)
array([[-0.5, -4. ],
       [-4.5, -2. ]])